• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.1-23
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• 2007

The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized $({\theta},\;{\eta},\;{\rho})-V-invexity$ assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.1-10
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• 2000

We obtain some duality results for nonsmooth multiobjective fractional programming problem under generalized invexity assumptions on the objective and constraint functions.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.433-455
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• 2005

Fritz John, and Karush-Kuhn-Tucker type optimality conditions for a constrained variational problem involving higher order derivatives are obtained. As an application of these Karush-Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type duals are formulated, and various duality relationships between the primal problem and each of the duals are established under invexity and generalized invexity. It is also shown that our results can be viewed as dynamic generalizations of those of the mathematical programming already reported in the literature.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.491-502
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• 2014

In this paper, by using the notion of ${\rho}$-(p,r)-invexity assumptions on the functions involved, optimality conditions and duality results (Mond-Weir, Wolfe and mixed type) are established on differentiable manifolds. Counterexample is constructed to justify that our investigations are more general than the existing work available in the literature.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.603-619
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• 2009

Wolfe and Mond-Weir type dual to a nondifferentiable continuous programming containing support functions are formulated and duality is investigated for these two dual models under invexity and generalized invexity. A close relationship of our duality results with those of nondifferentiable nonlinear programming problem is also pointed out.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.667-677
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• 2001

We consider a nonsmooth multiobjective opimization problem(PE) involving locally Lipschitz functions and define gen-eralized invexity for locally Lipschitz functions. Using Fritz John type optimality conditions, we establish Fritz John type sufficient optimality theorems for (PE) under generalized invexity.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1527-1534
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• 2010

In this paper, we consider nonsmooth optimization problem of which objective and constraint functions are locally Lipschitz. We establish sufficient optimality conditions and duality results for nonsmooth vector optimization problem given under nearly strict invexity and near invexity-infineness assumptions.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.85-107
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• 2007

In this paper, we develop a fairly large number of sets of global semiparametric sufficient efficiency conditions under various generalized (${\theta},{\eta},{\rho}$)-V-invexity assumptions for a multiobjective fractional programming problem involving arbitrary norms.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.273-281
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• 2003

The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.105-126
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• 2007

The purpose of this paper is to construct several parametric duality models and prove appropriate duality results under various generalized (${\theta},{\eta},{\rho}$)-V-invexity assumptions for a discrete minmax fractional programming problem involving arbitrary norms.